## ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

Choose the correct answer from the given four options (1-2):
Question 1.
Sum of rational number $$\frac { 5 }{ 7 }$$ and its additiveinverse is
(a) 1
(b) 0
(c) -1
(d) none of these
Solution:
Sum of $$\frac { 5 }{ 7 }$$ and its additive inverse.

Question 2.
Product of two rational numbers is 1. If oneof them is $$\frac { 4 }{ 5 }$$, then other is

Solution:
Product of two rational numbers = 1
One number = $$\frac { 4 }{ 5 }$$, then second number

Question 3.
Find the value of x for which $$\left(\frac{4}{9}\right)^{x} \times\left(\frac{3}{2}\right)^{-1}$$ = $$\frac{8}{27}$$.
Solution:

Comparing, we get
2x + 1 = 3
⇒ 2x = 3 – 1 = 2
⇒ x = $$\frac{2}{2}$$
∴ x = 1

Question 4.
Express the following numbers in standard form:
(i) 0.0000000000578
(ii) 345700000000000
Solution:
(i) 0.0000000000578 = 5.78 × 10-11
(ii) 345700000000000 = 3.457 × 1014

Question 5.
Insert ten rational numbers between $$\frac{-4}{5}$$ and $$\frac{2}{3}$$.
Solution:
Ten rational numbers between $$\frac{-4}{5}$$ and $$\frac{2}{3}$$
LCMof 5, 3 = 15

We take any 10 rational numbers among these.

Question 6.
Find the cube root of 50653.
Solution:
Cube root of 50653

Question 7.
Find the smallest number by which 3645 should be divided so that quotient is a perfect cube.
Solution:
3645
Factorising it we get

3645 = 3 × 3 × 3 × 3 × 3 × 3 × 5
Grouping the same kind of factors in 3’s,
we find that one factor 5 is left ungrouped.
So, dividing 3645 by 5, we get 729 which is a perfect cube
and its cube root is 3 × 3 = 9

Question 8.
If p = $$\frac{-3}{5}$$, q = $$\frac{1}{2}$$, r= $$\frac{-7}{9}$$,then verify p × (q + r) = p × q + p × r.
Solution:

Hence proved L.H.S. = R.H.S.

Question 9.
Find the square root of 7056 by prime factorisation method.
Solution:
Square root of 7056 = $$\sqrt{7056}$$

Question 10.
Find the least number which must be added to 59000 to make it a perfect square.
Solution:
59000
Taking the square root of 59000 by division method we find that

(242)2 < 59000 < (243)2
By adding 1449 – 1400 = 49
We shall get a perfect square 59049 and its square root = 243